BERLIN, May 15 (Reuters) - Germany's Social Democrats aim to win back working-class voters by promising to increase inheritance tax for the rich and abolish a flat-rate tax on investment income, a draft of its election manifesto seen by Reuters showed on Monday.

"We will tax large inheritances more strongly," said the draft manifesto of the SPD, which is junior partner in Chancellor Angela Merkel's governing coalition and whose leader Martin Schulz will run against her in the Sept. 24 election.

"For this, we want a comprehensive inheritance tax reform with high allowances so that the normal house from the parents or grandparents is not affected," the manifesto said.

The SPD also wants to abolish the flat-rate withholding tax on capital gains so that income from labour and capital will be taxed equally in the future.

The draft is expected to be approved by the SPD's party leadership next week and is likely to be adopted at a party congress on June 25.

Introduced in 2009 by former SPD finance minister Peer Steinbrueck to help fight tax evasion to countries like Switzerland and Luxemburg, withholding tax is charged at 25 percent on private income from capital gains. That is a lower rate than many workers pay in income tax, which is charged at progressive rates of up to 42 percent. (Reporting by Holger Hansen; Writing by Michael Nienaber; Editing by Catherine Evans)